Central Tendency

Measures of central tendency are ways of dealing with large sets of data and coming up with an amount to represent a typical piece of data from the set. The most common ways to measure central tendency are mean, median and mode.

Mean

The mean, or average, of a set of values is found by adding them up and dividing by the number of values in the set. For example, if you wanted to order a pizza and had a lot of spare time on your hands, you could call around to all the pizza places in town and get the price of a large pizza and put them in a list like this: (in dollars) 14, 12, 15, 13, 10. Now, if you wanted to know the mean price of a pizza, add those amounts up and divide by 5: 14 + 12 + 15 + 13 + 10 = 64; 64 ÷ 5 = 12.8 or $12.80

Median

The median price of a pizza would be the middle price if you put them in order. Let’s order the pizza prices above: 10, 12, 13, 14, 15. The middle value is 13, so that would be the median. I just remembered another pizza place that sells its pies for $10. Now our list is 10, 10, 12, 13, 14, 15. If you want to find the median of a list of values that is even, find the mean or halfway point between the two middle values. Here, they are 12 and 13, so halfway between them would be $12.50. Median is used most commonly when a few values are outliers that would skew the mean in one direction. They are used often when talking about things like salaries and home prices because a few very rich people can make the mean higher than most people’s salary or home price. Therefore, median is a more accurate way of showing a typical salary or home price.

Mode 

The mode is the value that appears most often in a list. In our list of pizza prices just above, 10 is the mode because it appears twice. Our original list of numbers had no mode because no values repeated.

Range

Range is the difference between the largest and the smallest number in a set of values. In our set of pizza prices, the largest is 15 and the smallest is 10, so the range is 5 (15 – 10).